.. role:: blue
   :class: blue


MbMesh Polygonal Object
=======================
.. _MbMesh_Polygonal_Object_:


.. kernel version: 


The :blue:`MbMesh` class is declared in the *mesh.h* file.

The :blue:`MbMesh` polygonal object is derived from the
:blue:`MbItem` class and is described by
a set of triangulations
RPArray< MbGrid > **grids**, a set of
polygons RPArray< MbPolygon3D > **wires**,
a set of apexes
RPArray< MbApex3D > **peaks**, a pointer to the
original object :ref:`MbRefItem <MbRefItem_Reference_Counter_>` *item*, the
*type*, a bounding cube **cube**, and the closed flag
*closed*.

A polygonal object is a set of triangular and
quadrilateral plates, polyline segments, and individual points. One of
the ways to construct a polygonal object is to approximate other
geometric model objects, for example, a solid. Each *i* -th face
of the solid is approximated by the triangulation **grids**\[*i*], each
*j*-th edge of the solid is approximated by the polygon
**wires**\[*j*], each *k*-th vertex of the solid
corresponds to the apex **peaks**\[*k*], and the closed flag
*closed* corresponds to whether the solid is closed. Another way
to obtain a polygonal object is to import data using
a polygonal representation converter.

The MbGrid triangulation represents
a set of points
SArray< MbFloatPoint3D > **points**,
the corresponding set of normals
SArray< MbFloatVector3D > **normals**
(the number of points equals the number of normals), a set of two-dimensional
points of the parametric domain of the surface
SArray< MbFloatPoint > **params** (the number
of two-dimensional points equals the number of three-dimensional points
or is zero -- the set may be empty), a set of triangular plates
SArray< MbTriangle > *triangles* as three
indices of the **points** set, and a set of quadrilateral
plates SArray< MbQuadrangle > *quadrangles* as
four indices of the **points** set. The plates of
the triangulation approximate a certain surface.

The :blue:`MbPolygon3D` polygon represents
an ordered set of points whose successive connection
produces a polyline approximating a certain curve.

The :blue:`MbApex3D` apex represents a point
endowed with additional data.

The pointer to the original object **item** may be null, and
the *type* may be undefined.

A vector image of a polygonal object is shown in Fig. 1.

.. figure:: /MODELER/OBJECTS_OF_GEOMETRIC_MODEL/pictures/O.8.5.1.png
   :width: 12cm
   :align: center

   Fig. 1

A shaded image of a polygonal object is shown in Fig. 2.

.. figure:: /MODELER/OBJECTS_OF_GEOMETRIC_MODEL/pictures/O.8.5.2.png
   :width: 12cm
   :align: center

   Fig. 2

Individual triangles of the object are visible in the figure because
the normal direction is constant in each triangle. If the normal
direction in the triangles of the triangulation changes continuously,
individual triangles of the object become invisible, see Fig. 3.

.. figure:: /MODELER/OBJECTS_OF_GEOMETRIC_MODEL/pictures/O.8.5.3.png
   :width: 12cm
   :align: center

   Fig. 3

A polygonal object can be created by the
:blue:`MbItem`:: :blue:`CreateMesh`\() method or by the
:blue:`MbItem`:: :blue:`AddYourMesh`\() method.
A polygonal object is used for visualization, computations, and
manufacturing of modeled objects. The main advantage of
a polygonal object is its simplicity and high computational speed,
for example, for intersection with a line.